Blorst horst.

I would like it if you paired each "myth" line with an explicit "truth" line that gave the tl;dr for us, maybe even using simple language e.g.

Myth: The cardinalities of infinite sets can be compared like ordinary numbers. Reality: If the axiom of choice is false, you can have one set's cardinality be both larger and smaller than another's

(maybe even a short blurb explaining the axiom of choice's role)

I could still understand you, but it certainly helped that I'd borrowed my friend's topology book over the summer.

Rather than making a big list, some more structure and an actual conclusion to topic #1 would have helped cement things in my brain.

Since this turned out pretty long, you could actually split the topics into separate posts in a series. And with a little editing I would be all for these being top-level posts rather than discussion secion.